Alternative dynamics such as the death-birth [1]} and the pairwise comparison [2]} could potentially hold similar fixation functions to the ones reported here. Additionally, considering multiplayer social dilemmas in well mixed populations would allow transition probability ratios \(\gamma _k^N\)  to have a non-monotonic dependence on \(k\)  [3]}, [4]}, which could lead to the emergence of new fixation probability functions of population size. Finally, fixation probabilities have been studied in the context of structured populations as well, often holding distinctive dependences on population size [5]}, [6]}, [7]}, [8]}. Expanding our analysis to structured populations could hold new effects and lead to a more general theory of fixation probability functions.
